Question

Muralists will often make a scale drawing of an art piece before creating the large finished version. A muralist has sketched an art piece on a sheet of drawing paper that is 5 feet by 6 feet.

If the final mural will be 65 feet by 78 feet, what is the scale factor for this dilation.

The scale factor is
.

The owner of the wall has decided to only give permission to paint on the lower half of the wall. Can the muralist simply use the transformation (x,y) arrowright parenleftx ,
1
2
yparenright in addition to the scale factor to alter the sketch for use in the allowed space? Select the correct explanation.

A The mural will not be distorted, both sides will be changed evenly.
B The mural will be distorted. This mapping will shrink the height of the mural in half, but by keeping the original width, the shapes will change.
C The mural will be distorted. This mapping will shrink the height and width of the mural in half, but by changing the original width, the shapes will change.
D The mural will be distorted. This mapping will shrink the width of the mural in half, but by keeping the original height, the shapes will change.

Answer 1

Scale ratios are used to enlarge or compress a shape.

• The scale factor is 13.
• The transformation rule is $(x,y) \to 13(x,y)$.
• The mural will not distorted, because the sides are changed evenly.

Given

$Scale = 5ft:6ft$

$Final = 65ft:78ft$

To get the scale factor (k), we simply divide the final measurement by the scale measurement.

So, we have:

$k = \frac{Final}{Scale}$

For the length, we have:

$k = \frac{65ft}{5ft}$

$k = 13$

For the width, we have:

$k = \frac{78ft}{6ft}$

$k = 13$

Hence, the scale factor is 13

And the transformation is:

$(x,y) \to 13(x,y)$

This implies that, the muralist can apply $(x,y) \to k(x,y)$ for the transformation

Hence;

(a) The mural will not distorted, because the sides are changed evenly.

Read more about scale ratios at:

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